Everything you say makes sense, but, you can't really use the 10-22 on a FF while you can use the 16-35 on an APS-C body (effective range 26-56). Instead of needing 2 bodies to get a wide angle option, you only need one. And, the 16-35 is faster.
So, part of this depends on what you have glass wise and part on what you are shooting. As far as any distortion is concerned, LR, PS, DXO and other options deal with this quite effectively. I owned and really liked the 10-22 when I had a crop body, but am really happier with FF.